maths and calculation policy - st john's watford primary ... · • effectively scaffolded and...

St John’s Church of England Primary School

Maths and Calculation Policy

Date Approved: 27th March 2019

Headteacher: Mrs Helen Langeveld

Chair of Governors: Mrs Julie Griffiths

Review Date: 26th March 2022

Love, Respect, Value

St John’s Church of England Primary School is committed to high expectations for all and to embracing equality.

St John’s C of E Primary School Maths and Calculation Policy

Our Vision:

Through ‘Growing Together in Love and Respect’, we provide the opportunity for every child to reach their full potential. We embrace Christian values and ensure all children are ready for their next steps in a learning environment that provides a balance between skills, knowledge, learning from and embracing mistakes and mastery approach.

Rationale Mathematics equips pupils with the uniquely powerful set of tools to understand and change the world. These tools include logical reasoning, problem solving skills and the ability to think in abstract ways.

Mathematics is important in everyday life. It is integral to all aspects of life and with this in mind we endeavour to ensure that children develop a positive and enthusiastic attitude towards mathematics that will stay with them.

The National Curriculum for mathematics describes in detail what pupils must learn in each year group. Combined with our Calculation Policy, this ensures continuity and progression and high expectations for attainment in mathematics.

It is vital that a positive attitude towards mathematics is encouraged amongst all of our pupils in order to foster confidence and achievement in a skill that is essential in our society. At St John’s we use the Early Years Foundation Stage (2017) and the National Curriculum for Mathematics (2014) as the basis of our mathematics programme and the HFL Essential planning. We also use Numicon approaches to further extend planning and mathematical opportunities. We aim for all pupils to achieve mastery in the key concepts of mathematics, appropriate for their age group, in order that they make genuine progress and avoid gaps in their understanding that provide barriers to learning as they move through education. Assessment for Learning, an emphasis on investigation, problem solving and the development of mathematical thinking and a rigorous approach to the development of teacher subject knowledge are therefore essential components to successful mathematics at St John’s school.

The calculation part of the policy outlines a model progression through written strategies for addition, subtraction, multiplication and division. Through the policy, we aim to link concrete manipulatives and representations in order that the children can be vertically accelerated through each strand of calculation. We know that school wide policies, such as this, can ensure consistency of approach, enabling children to progress stage by stage through models and representations they recognise from previous teaching, allowing for deeper conceptual understanding and fluency. Teachers will be presenting strategies and equipment appropriate to children’s level of understanding to allow for both support and challenge. However, it is expected that the majority of children in each class will be working at age-appropriate levels as set out in the National Curriculum and in line with school policy.

Aims

We aim to provide the pupils with a mathematics curriculum and high quality teaching to produce individuals who are numerate, creative, independent, inquisitive, enquiring and confident. We also aim to provide a stimulating environment and adequate resources so that pupils can develop their mathematical skills to the full.

Our pupils should:

• have a well-developed sense of the size of a number and where it fits into the number system • know by heart number facts such as number bonds, multiplication tables, doubles and halves • use what they know by heart to figure out numbers mentally • calculate accurately and efficiently, both mentally and in writing and paper, • drawing on a range of calculation strategies • recognise when it is appropriate to use a calculator and be able to do so effectively • make sense of number problems, including non-routine/’real’ problems and identify the operations needed to solve them


• explain their methods and reasoning, using correct mathematical terms • judge whether their answers are reasonable and have strategies for checking them where necessary • suggest suitable units for measuring and make sensible estimates of measurements • collect data and select methods to present appropriately • explain and make predictions from the numbers in graphs, diagrams, charts and tables • develop spatial awareness and an understanding of the properties of 2d and 3d shapes

Provision Pupils are provided with a variety of opportunities to develop and extend their Mathematical skills, including:

• Group work • Paired work • Whole class teaching • Individual work including 1:1 tuition

Pupils engage in:

• the development of mental strategies • written methods • practical work • investigational work • problem solving • mathematical discussion • consolidation of basic skills and number facts • maths games

We recognise the importance of establishing a secure foundation in mental calculation and recall of number facts before standard written methods are introduced. We use accurate mathematical vocabulary in our teaching and children are expected to use it in their verbal and written explanations.

Mathematics contributes to many subjects and it is important the children are given opportunities to apply and use Mathematics in real contexts. It is important that time is found in other subjects for pupils to develop their Numeracy Skills, e.g. there should be regular, carefully planned opportunities for measuring in science and technology, for the consideration of properties of shape and geometric patterns in technology and art, and for the collection and presentation of data in science, history and geography.

We endeavour at all times to set work that is challenging, motivating and encourages the pupils to think about how they learn and to talk about what they have been learning. Additional enrichment opportunities are provided for pupils to further develop mathematical thinking e.g. through cooking, music, and maths investigations and games.

Teachers plan problem solving and investigational activities throughout each unit to ensure that pupils develop the skills of mathematical thinking and enquiry.

To provide adequate time for developing mathematics, maths is taught daily and discretely. Maths lessons may vary in length but will usually last for about 30 minutes in Early Years Foundation Stage, 45 minutes in Key Stage 1 and 60 minutes in Key Stage 2.

Teaching Approaches

Teachers use a range of teaching strategies to engage the children in maths and ensure progress is made by all children within a class; no set formula is used. A typical lesson would include:

• Both teaching input and pupil activities, • A balance between whole class, guided grouped and independent work, (groups, pairs and individual work)


• effectively scaffolded and differentiated activities/objectives and appropriate challenge.

Sometimes the focus for the session is new learning, at other times pupils may be practising, to master the application of a concept they have learned earlier. The focus of the session may vary for different children depending on their learning needs.

At times there may be opportunities to develop skills and understanding of mathematics through additional activities, some of which may take place at home.

Assessment

Formative Assessment Teachers integrate the use of formative assessment strategies such as effective questioning, clear learning objectives, the use of success criteria and effective feedback and response in their teaching.

Summative Assessment Using termly assessments (currently Headstart), pupils are assessed against Age Related Expectations. The school’s MIS progress tracking system is updated termly. National Curriculum tests are used at the end of KS1 and 2; teachers use past questions and papers throughout the year as a part of the teaching and learning to inform their assessments as they prepare pupils for these assessments.

All assessments and teaching informs teachers understanding of a child’s attainment in maths and this is recorded on the school’s MIS progress tracking system

The school’s Assessment, Feedback and Reporting Policy informs high quality feedback and pupils’ response to it in Mathematics.

Early Years Foundation Stage (EYFS)

We follow EYFS curriculum guidance for Mathematics. However, we are committed to ensuring the confident development of number sense and put emphasis on mastery of key early concepts. Pupils will explore numbers to 20 with a key focus on understanding to 10 and the development of models and images for numbers as a solid foundation for further progress. They will be taught basic 2d and 3d shape names and an understanding of the properties, as well as non standard measures, weight and capacity.

Resources

A bank of essential concrete mathematical resources including Numicon, Cuisenaire rods , bead strings, multi link etc are available in every classroom to be used as day to day resources. Further resources supporting whole school requirements are kept in the Sky Floor (blue Level 2) resource cupboard.

Role of the Subject Leader

• Ensures teachers understand the requirements of the National Curriculum and helps them to plan lessons. • Leads by example by setting high standards in their own teaching. • Prepares, organises and leads CPD and joint professional development. • Works with the SENCO • Observes colleagues from time to time with a view to identifying the support they need. • Attends CPD and feeds back for whole school impact • Keeps parents informed about Mathematics issues and promote parental engagement • Discusses regularly with the Headteacher and the governors the progress of whole school maths. • Deploys support staff to address mathematics related needs within the school.


• Monitors and evaluates mathematics provision in the school by conducting regular work scrutiny, learning walks and assessment data analysis.

The importance of mental mathematics While this policy focuses on written calculations in mathematics, we recognise the importance of the mental strategies and known facts that form the basis of all calculations. The following checklists outline the key skills and number facts that children are expected to develop throughout the school. To add and subtract successfully, children should be able to:

· recall all addition pairs to 9 + 9 and number bonds to 10 · recognise addition and subtraction as inverse operations · add mentally a series of one digit numbers (e.g. 5 + 8 + 4) · add and subtract multiples of 10 or 100 using the related addition fact and their knowledge of place value

(e.g. 600 + 700, 160 — 70) · partition 2 and 3 digit numbers into multiples of 100, 10 and 1 in different ways

(e.g. partition 74 into 70 + 4 or 60 + 14) · use estimation by rounding to check answers are reasonable

To multiply and divide successfully, children should be able to:

· add and subtract accurately and efficiently · recall multiplication facts to 12 x 12 = 144 and division facts to 144 ÷ 12 = 12 · use multiplication and division facts to estimate how many times one number divides into another etc. · know the outcome of multiplying by 0 and by 1 and of dividing by 1 · understand the effect of multiplying and dividing whole numbers by 10, 100 and later 1000 · recognise factor pairs of numbers (e.g. that 15 = 3 x 5, or that 40 = 10 x 4) and increasingly able to recognise

common factors · derive other results from multiplication and division facts and multiplication and division by 10 or 100 (and

later 1000) · notice and recall with increasing fluency inverse facts · partition numbers into 100s, 10s and 1s or multiple groupings · understand how the principles of commutative, associative and distributive laws apply or do not apply to

multiplication and division · understand the effects of scaling by whole numbers and decimal numbers or fractions · understand correspondence where n objects are related to m objects · investigate and learn rules for divisibility

Progression in addition and subtraction

Addition and subtraction are connected.

Addition names the whole in terms of the parts and subtraction names a missing part of the whole.


Addition Subtraction Combining two sets (aggregation) Putting together – two or more amounts or numbers are put together to make a total 7 + 5 = 12

Count one set, then the other set. Combine the sets and count again. Starting at 1. Counting along the bead bar, count out the 2 sets, then draw them together, count again. Starting at 1.

Taking away (separation model) Where one quantity is taken away from another to calculate what is left. 7 – 2 = 5

Multilink towers - to physically take away objects.

Combining two sets (augmentation) This stage is essential in starting children to calculate rather than counting Where one quantity is increased by some amount. Count on from the total of the first set, e.g. put 3 in your head and count on 2. Always start with the largest number. Counters:

Start with 7, then count on 8, 9, 10, 11, 12 Bead strings:

Make a set of 7 and a set of 5. Then count on from 7.

Finding the difference (comparison model) Two quantities are compared to find the difference. 8 – 2 = 6 Counters: Bead strings:

Make a set of 8 and a set of 2. Then count the gap.

Multilink Towers:

Multilink Towers:


Cuisenaire Rods:

Number tracks:

Start on 5 then count on 3 more

Cuisenaire Rods:

Number tracks: Start with the smaller number and count the gap to the larger number. 1 set within another (part-whole model) The quantity in the whole set and one part are known, and may be used to find out how many are in the unknown part. 8 – 2 = 6 Counters:

Bead strings:

Bridging through 10s St John’s C of E Primary School Maths and Calculation Policy

This stage encourages children to become more efficient and begin to employ known facts. Bead string:

7 + 5 is decomposed / partitioned into 7 + 3 + 2. The bead string illustrates ‘how many more to the next multiple of 10?’ (children should identify how their number bonds are being applied) and then ‘if we have used 3 of the 5 to get to 10, how many more do we need to add on? (ability to decompose/partition all numbers applied) Number track:

Steps can be recorded on a number track alongside the bead string, prior to transition to number line. Number line

Bead string:

12 – 7 is decomposed / partitioned in 12 – 2 – 5. The bead string illustrates ‘from 12 how many to the last/previous multiple of 10?’ and then ‘if we have used 2 of the 7 we need to subtract, how many more do we need to count back? (ability to decompose/partition all numbers applied) Number Track: Steps can be recorded on a number track alongside the bead string, prior to transition to number line. Number Line:

Counting up or ‘Shop keepers’ method Bead string: 12 – 7 becomes 7 + 3 + 2. Starting from 7 on the bead string ‘how many more to the next multiple of 10?’ (children should recognise how their number bonds are being applied), ‘how many more to get to 12?’. Number Track: Number Line:


Compensation model (adding 9 and 11) (optional) This model of calculation encourages efficiency and application of known facts (how to add ten)

7 + 9 Bead string:

Children find 7, then add on 10 and then adjust by removing 1. Number line:

18 – 9 Bead string:

Children find 18, then subtract 10 and then adjust by adding 1. Number line:


Working with larger numbers

Tens and ones + tens and ones Ensure that the children have been transitioned onto Base 10 equipment and understand the

abstract nature of the single ‘tens’ sticks and ‘hundreds’ blocks Partitioning (Aggregation model) 34 + 23 = 57 Base 10 equipment:

Children create the two sets with Base 10 equipment and then combine; ones with ones, tens with tens. Partitioning (Augmentation model) Base 10 equipment: Encourage the children to begin counting from the first set of ones and tens, avoiding counting from 1. Beginning with the ones in preparation for formal columnar method.

Number line:

At this stage, children can begin to use an informal method to support, record and explain their method. (optional) 30 + 4 + 20 + 3

Take away (Separation model) 57 – 23 = 34 Base 10 equipment: Children remove the lower quantity from the larger set, starting with the ones and then the tens. In preparation for formal decomposition.

Number Line:

At this stage, children can began to use an informal method to support, record and explain their method (optional) (50 + 7) - (20 + 3) 30 4 34


Bridging with larger numbers

Once secure in partitioning for addition, children begin to explore exchanging. What happens if the ones are greater than 10? Introduce the term ‘exchange’. Using the Base 10 equipment, children exchange ten ones for a single tens rod, which is equivalent to crossing the tens boundary on the

bead string or number line. Base 10 equipment: 37 + 15 = 52

Discuss counting on from the larger number irrespective of the order of the calculation.

Base 10 equipment: 52 – 37 = 15

Expanded Vertical Method (optional) Children are then introduced to the expanded vertical method to ensure that they make the link

between using Base 10 equipment, partitioning and recording using this expanded vertical method.

Base 10 equipment: 67 + 24 = 91

Base 10 equipment: 91 – 67 = 24

90 + 1 - 60 + 7 20 + 4


Compact method

Compact decomposition


Vertical acceleration

By returning to earlier manipulative experiences children are supported to make links across mathematics, encouraging ‘If I know this…then I also know…’ thinking.

Decimals Ensure that children are confident in counting forwards and backwards in decimals – using bead

strings to support. Bead strings:

Each bead represents 0.1, each different block of colour equal to 1.0 Base 10 equipment:

Addition of decimals Aggregation model of addition Counting both sets – starting at zero. 0.7 + 0.2 = 0.9

Augmentation model of addition Starting from the first set total, count on to the end of the second set. 0.7 + 0.2 = 0.9

Bridging through 1.0 Encouraging connections with number bonds. 0.7 + 0.5 = 1.2

Partitioning 3.7 + 1.5 = 5.2

Subtraction of decimals Take away model 0.9 – 0.2 = 0.7 Finding the difference (or comparison model): 0.8 – 0.2 = Bridging through 1.0 Encourage efficient partitioning. 1.2 – 0.5 = 1.2 – 0.2 – 0.3 = 0.7 Partitioning 5.7 – 2.3 = 3.4


Gradation of difficulty- addition: 1. No exchange 2. Extra digit in the answer 3. Exchanging ones to tens 4. Exchanging tens to hundreds 5. Exchanging ones to tens and tens to hundreds 6. More than two numbers in calculation 7. As 6 but with different number of digits 8. Decimals up to 2 decimal places (same number of decimal places) 9. Add two or more decimals with a range of decimal places

Gradation of difficulty- subtraction: 1. No exchange 2. Fewer digits in the answer 3. Exchanging tens for ones 4. Exchanging hundreds for tens 5. Exchanging hundreds to tens and tens to ones 6. As 5 but with different number of digits 7. Decimals up to 2 decimal places (same number of decimal places) 8. Subtract two or more decimals with a range of decimal places


Progression in Multiplication and Division

Multiplication and division are connected. Both express the relationship between a number of equal parts and the whole.

Part

Part

Part

Part

Whole

The following array, consisting of four columns and three rows, could be used to represent the number sentences: - 3 x 4 = 12, 4 x 3 =12, 3 + 3 + 3 + 3 = 12, 4 + 4 + 4 =12. And it is also a model for division 12 ÷ 4 = 3 12 ÷ 3 = 4 12 – 4 – 4 – 4 = 0 12 – 3 – 3 – 3 – 3 = 0


Multiplication Division Early experiences Children will have real, practical experiences of handling equal groups of objects and counting in 2s, 10s and 5s. Children work on practical problem solving activities involving equal sets or groups.

Children will understand equal groups and share objects out in play and problem solving. They will count in 2s, 10s and 5s.

Repeated addition (repeated aggregation) 3 times 5 is 5 + 5 + 5 = 15 or 5 lots of 3 or 5 x 3 Children learn that repeated addition can be shown on a number line.

Children learn that repeated addition can be shown on a bead string.

Children also learn to partition totals into equal trains using Cuisenaire Rods

Sharing equally 6 sweets get shared between 2 people. How many sweets do they each get? A bottle of fizzy drink shared equally between 4 glasses.

Grouping or repeated subtraction There are 6 sweets. How many people can have 2 sweets each?


Scaling This is an extension of augmentation in addition, except, with multiplication, we increase the quantity by a scale factor not by a fixed amount. For example, where you have 3 giant marbles and you swap each one for 5 of your friend’s small marbles, you will end up with 15 marbles. This can be written as: 1 + 1 + 1 = 3 scaled up by 5 5 + 5 + 5 = 15

For example, find a ribbon that is 4 times as long as the blue ribbon.

We should also be aware that if we multiply by a number less than 1, this would correspond to a scaling that reduces the size of the quantity. For example, scaling 3 by a factor of 0.5 would reduce it to 1.5, corresponding to 3 x 0.5 = 1.5.

Repeated subtraction using a bead string or number line 12 ÷ 3 = 4

The bead string helps children with interpreting division calculations, recognising that 12 ÷ 3 can be seen as ‘how many 3s make 12?’ Cuisenaire Rods also help children to interpret division calculations.

Grouping involving remainders Children move onto calculations involving remainders. 13 ÷ 4 = 3 r1

Or using a bead string see above.

Commutativity Children learn that 3 x 5 has the same total as 5 x 3. This can also be shown on the number line. 3 x 5 = 15 5 x 3 = 15

Children learn that division is not commutative and link this to subtraction.

Arrays Children learn to model a multiplication calculation using an array. This model supports their understanding of commutativity and the development of the grid in a written method. It also supports the finding of factors of a number.

Children learn to model a division calculation using an array. This model supports their understanding of the development of partitioning and the ‘bus stop method’ in a written method. This model also connects division to finding fractions of discrete


quantities.

Inverse operations Trios can be used to model the 4 related multiplication and division facts. Children learn to state the 4 related facts. 3 x 4 = 12 4 x 3 = 12 12 ÷ 3 = 4 12 ÷ 4 = 3 Children use symbols to represent unknown numbers and complete equations using inverse operations. They use this strategy to calculate the missing numbers in calculations. x 5 = 20 3 x ∆ = 18 O x = 32 24 ÷ 2 = 15 ÷ O = 3 ∆ ÷ 10 = 8

This can also be supported using arrays: e.g. 3 X ? = 12

Partitioning for multiplication Arrays are also useful to help children visualise how to partition larger numbers into more useful representation. 9 x 4 = 36

Children should be encouraged to be flexible with how they use number and can be encouraged to break the array into more manageable chunks. 9 x 4 =

Which could also be seen as 9 x 4 = (3 x 4) + (3 x 4) + (3 x 4) = 12 + 12 + 12 = 36 Or 3 x (3 x 4) = 36 And so 6 x 14 = (2 x 10) + (4 x 10) + (4 x 6) = 20 + 40 + 24 = 84

Partitioning for division The array is also a flexible model for division of larger numbers 56 ÷ 8 = 7

Children could break this down into more manageable arrays, as well as using their understanding of the inverse relationship between division and multiplication. 56 ÷ 8 = (40 ÷ 8) + (16 ÷ 8) = 5 + 2 = 7


To be successful in calculation learners must have plenty of experiences of being flexible with partitioning, as this is the basis of distributive and associative law. Associative law (multiplication only) :- E.g. 3 x (3 x 4) = 36 The principle that if there are three numbers to multiply these can be multiplied in any order. Distributive law (multiplication):- E.g. 6 x 14 = (2 x 10) + (4 x 10) + (4 x 6) = 20 + 40 + 24 = 84 This law allows you to distribute a multiplication across an addition or subtraction. Distributive law (division):- E.g. 56 ÷ 8 = (40 ÷ 8) + (16 ÷ 8) = 5 + 2 = 7 This law allows you to distribute a division across an addition or subtraction.

Arrays leading into the grid method Children continue to use arrays and partitioning, where appropriate, to prepare them for the grid method of multiplication. Arrays can be represented as ‘grids’ in a shorthand version and by using place value counters to show multiples of ten, hundred etc.

Arrays leading into chunking and then long and short division Children continue to use arrays and partitioning where appropriate, to prepare them for the ‘chunking’ and short method of division. Arrays are represented as ‘grids’ as a shorthand version. e.g. 78 ÷ 3 =

78 ÷ 3 = (30 ÷ 3) + (30 ÷ 3) + (18 ÷ 3) = 10 + 10 + 6 = 26


Grid method This written strategy is introduced for the multiplication of TO x O to begin with. It may require column addition methods to calculate the total.

The vertical method- ‘chunking’ leading to long division See above for example of how this can be modelled as an array using place value counters. 78 ÷ 3 =

Short multiplication — multiplying by a single digit The array using place value counters becomes the basis for understanding short multiplication first without exchange before moving onto exchanging 24 x 6

Short division — dividing by a single digit Whereas we can begin to group counters into an array to show short division working 136 ÷ 4


Gradation of difficulty (short multiplication) 1. TO x O no exchange

2. TO x O extra digit in the answer

3. TO x O with exchange of ones into tens

4. HTO x O no exchange

5. HTO x O with exchange of ones into tens

6. HTO x O with exchange of tens into hundreds

7. HTO x O with exchange of ones into tens and tens into hundreds

8. As 4-7 but with greater number digits x O

9. O.t x O no exchange

10. O.t with exchange of tenths to ones

11. As 9 - 10 but with greater number of digits which may include a range of decimal places x O

Gradation of difficulty (short division) 1. TO ÷ O no exchange no remainder

2. TO ÷ O no exchange with remainder

3. TO ÷ O with exchange no remainder

4. TO ÷ O with exchange, with remainder

5. Zero in the quotient e.g. 816 ÷ 4 = 204

6. As 1-5 HTO ÷ O

7. As 1-5 greater number of digits ÷ O

8. As 1-5 with a decimal dividend e.g. 7.5 ÷ 5 or 0.12 ÷ 3

9. Where the divisor is a two digit number

See below for gradation of difficulty with remainders

Dealing with remainders

Remainders should be given as integers, but children need to be able to decide what to do after division, such as rounding up or down accordingly. e.g.:

· I have 62p. How many 8p sweets can I buy?


· Apples are packed in boxes of 8. There are 86 apples. How many boxes are needed?

Gradation of difficulty for expressing remainders 1. Whole number remainder 2. Remainder expressed as a fraction of the

divisor 3. Remainder expressed as a simplified fraction 4. Remainder expressed as a decimal

Long multiplication—multiplying by more than one digit Children will refer back to grid method by using place value counters or Base 10 equipment with no exchange and using synchronised modelling of written recording as a long multiplication model before moving to TO x TO etc.

Long division —dividing by more than one digit Children should be reminded about partitioning numbers into multiples of 10, 100 etc. before recording as either:- 1. Chunking model of long division using Base

10 equipment 2. Sharing model of long division using place

value counters See the following pages for exemplification of these methods.

Chunking model of long division using Base 10 equipment This model links strongly to the array representation; so for the calculation 72 ÷ 6 = ? - one side of the array is unknown and by arranging the Base 10 equipment to make the array we can discover this unknown. The written method should be written alongside the equipment so that children make links. Begin with divisors that are between 5 and 9 1. Make a rectangle where one side is 6 (the

number dividing by) – grouping 6 tens

After grouping 6 lots of 10 (60) we have 12 left over


2. Exchange the remaining ten for ten ones 3.

4. Complete the rectangle by grouping the remaining ones into groups of 6

Move onto working with divisors between 11 and 19 Children may benefit from practise to make multiples of tens using the hundreds and tens and tens and ones. 1. Make a rectangle where one side is 12 (the

number dividing by) using hundreds and tens


With 49 remaining

2. Make groups of 12 using tens and ones No more groups of 12 can be made and 1 remains

Sharing model of long division using place value counters Starting with the most significant digit, share the hundreds. The writing in brackets is for verbal explanation only. St John’s C of E Primary School Maths and Calculation Policy

Moving to tens – exchanging hundreds for tens means that we now have a total of 13 tens counters (hence the arrow) Moving to ones, exchange tens to ones means that we now have a total of 12 ones counters (hence the arrow)


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